The High Deflection Constant Speed Universal Joint of my U.S. Pat. No. 3,924,420 can be used to interconnect driving and driven shafts which have the axes thereof displaced by relatively-large angles. In addition, that universal joint will cause the driven shaft to move at the same speed as the driving shaft and to be free of acceleration and deceleration forces during each revolution thereof. However, that High Deflection Constant Speed Universal Joint cannot be used to interconnect driving and driven shafts which have the axes thereof displaced by angles as large as 90.degree.. Further, that High Deflection Constant Speed Univeral Joint, and all other prior universal joints of which I am aware, have only three axes about which the torque transmitting components thereof can oscillate relative to each other.